Keiju Murata

CFT Duals for Extreme Black Holes

It is argued that the general four-dimensional extremal Kerr-Newman-AdS-dS black hole is holographically dual to a (chiral half of a) two-dimensional CFT, generalizing an argument given recently for the special case of extremal Kerr. Specifically, the asymptotic symmetries of the near-horizon region of the general extremal black hole are shown to be generated by a Virasoro algebra. Semiclassical formulae are derived for the central charge and temperature of the dual CFT as functions of the cosmological constant, Newtons constant and the black hole charges and spin. We then show, assuming the Cardy formula, that the microscopic entropy of the dual CFT precisely reproduces the macroscopic Bekenstein-Hawking area law. This CFT description becomes singular in the extreme Reissner-Nordstrom limit where the black hole has no spin. At this point a second dual CFT description is proposed in which the global part of the U(1) gauge symmetry is promoted to a Virasoro algebra. This second description is also found to reproduce the area law. Various further generalizations including higher dimensions are discussed.

Central charges in extreme black hole/CFT correspondence

The Kerr/CFT correspondence has been recently broadened to the general extremal black holes under the assumption that the central charges from the non-gravitational fields vanish. To confirm this proposal, we derive the expression of the conserved charges in the Einstein-Maxwell-scalar theory with topological terms in four and five dimensions and check that the above assumption was correct. Combining the computed central charge with the expected form of the temperature, the Bekenstein-Hawking entropy of the general extremal black holes in four and five dimensions can be reproduced by using the Cardy formula.

Hawking radiation from rotating black holes and gravitational anomalies

We study the Hawking radiation from Rotating black holes from the gravitational anomalies point of view. First, we show that the scalar field theory near the Kerr black hole horizon can be reduced to the 2-dimensional effective theory. Then, following Robinson and Wilczek, we derive the Hawking flux by requiring the cancellation of gravitational anomalies. We also apply this method to Hawking radiation from higher dimensional Myers-Perry black holes. In the appendix, we present the trace anomaly derivation of Hawking radiation to argue the validity of the boundary condition at the horizon.

Non-equilibrium Condensation Process in a Holographic Superconductor

We study the non-equilibrium condensation process in a holographic superconductor. When the temperature T is smaller than a critical temperature Tc, there are two black hole solutions, the Reissner-Nordström-AdS black hole and a black hole with a scalar hair. In the boundary theory, they can be regarded as the supercooled normal phase and the superconducting phase, respectively. We consider perturbations on supercooled Reissner-Nordström-AdS black holes and study their non-linear time evolution to know about physical phenomena associated with rapidly-cooled superconductors. We find that, for T < Tc, the initial perturbations grow exponentially and, eventually, spacetimes approach the hairy black holes. We also clarify how the relaxation process from a far-from-equilibrium state proceeds in the boundary theory by observing the time dependence of the superconducting order parameter. Finally, we study the time evolution of event and apparent horizons and discuss their correspondence with the entropy of the boundary theory. Our result gives a first step toward the holographic understanding of the non-equilibrium process in superconductors.

What happens at the horizon(s) of an extreme black hole

A massless scalar field exhibits an instability at the event horizon of an extreme black hole. We study numerically the nonlinear evolution of this instability for spherically symmetric perturbations of an extreme Reissner–Nordstrom (RN) black hole. We find that generically the endpoint of the instability is a non-extreme RN solution. However, there exist fine-tuned initial perturbations for which the instability never decays. In this case, the perturbed spacetime describes a time-dependent extreme black hole. Such solutions settle down to extreme RN outside, but not on, the event horizon. The event horizon remains smooth but certain observers who cross it at late time experience large gradients there. Our results indicate that these dynamical extreme black holes admit a C1 extension across an inner (Cauchy) horizon.

On the horizon instability of an extreme Reissner-Nordström black hole

A bstractAretakis has proved that a massless scalar field has an instability at the horizon of an extreme Reissner-Nordström black hole. We show that a similar instability occurs also for a massive scalar field and for coupled linearized gravitational and electromagnetic perturbations. We present numerical results for the late time behaviour of massless and massive scalar fields in the extreme RN background and show that instabilities are present for initial perturbations supported outside the horizon, e.g. an ingoing wavepacket. For a massless scalar we show that the numerical results for the late time behaviour are reproduced by an analytic calculation in the near-horizon geometry. We relate Aretakis’ conserved quantities at the future horizon to the Newman-Penrose conserved quantities at future null infinity.

Anisotropic inflation with non-abelian gauge kinetic function

We study an anisotropic inflation model with a gauge kinetic function for a non-abelian gauge field. We find that, in contrast to abelian models, the anisotropy can be either a prolate or an oblate type, which could lead to a different prediction from abelian models for the statistical anisotropy in the power spectrum of cosmological fluctuations. During a reheating phase, we find chaotic behaviour of the non-abelian gauge field which is caused by the nonlinear self-coupling of the gauge field. We compute a Lyapunov exponent of the chaos which turns out to be uncorrelated with the anisotropy.

Hawking radiation from black rings

We calculate the quantum radiation from the 5-dimensional charged rotating black rings by demanding the radiation eliminate the possible anomalies on the horizons. It is shown that the temperature, energy flux, and angular-momentum flux exactly coincide with those of the Hawking radiation. The black rings considered in this paper contain the Myers-Perry black hole as a limit, and the quantum radiation for this black hole, obtained in the literature, is recovered in the limit. The results support the picture that the Hawking radiation can be regarded as the anomaly eliminator on horizons and suggest its general applicability to the higher-dimensional black holes discovered recently.

Black Hole Instabilities and Local Penrose Inequalities

Various higher-dimensional black holes have been shown to be unstable by studying linearized gravitational perturbations. A simpler method for demonstrating instability is to find initial data that describes a small perturbation of the black hole and violates a Penrose inequality. An easy way to construct initial data is by conformal rescaling of the unperturbed black hole initial data. For a compactified black string, we construct initial data which violates the inequality almost exactly where the Gregory–Laflamme instability appears. We then use the method to confirm the existence of the ‘ultraspinning’ instability of Myers–Perry black holes. Finally, we study black rings. We show that ‘fat’ black rings are unstable. We find no evidence of any rotationally symmetric instability of ‘thin’ black rings.

Stability of Five-Dimensional Myers-Perry Black Holes with Equal Angular Momenta

We study the stability of five-dimensional Myers-Perry black holes with equal angular momenta which have an enlarged symmetry, U(2). Using this symmetry, we derive master equations for the metric perturbations that are relevant to the stability. Using the master equations, we prove the stability of Myers-Perry black holes under these perturbations. Our results provide evidence on the stability of Myers-Perry black holes with equal angular momenta.